Design of Three-Dimensional Superresolution Filters and Limits of Axial Optical Superresolution

Theories to design a three-dimensional superresolution filter (TDSF) for confocal microscopy are proposed that can obtain a globally optimal solution through linear programming. The designed TDSF is proved to be a phase-only element introducing a phase delay of 0 or (pi). Five design examples of the TDSF are presented to demonstrate the validity of these theories. Regardless of transverse superresolution, a curve of Seu (Ga +-) defined as the maximum value of Strehl ratio S under the axial resolving power of Ga +- is calculated to set the fundamental limits of axial optical superresolution. Finally, what is to our knowledge a novel analytic expression of Seu (Ga +-) is deduced.